On Two Truncated Quintuple Series Theorems

Abstract

We investigate two truncated series derived recently by S. H. Chan, T. P. N. Ho, and R. Mao from the Watson quintuple product identity and experimentally discover two stronger results. In this context, for each $S\in \{1,2\}$, we obtain two infinite families of linear homogeneous inequalities for the number of partitions of n into parts congruent to $\pm S\mathrm{mod}5$.

Keywords:

• theta series
• quintuple product identity
• Rogers-Ramanujan functions

MSC 2010:

• 05A17
• 05A19
• 05A015
• 05A20